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PARAMETRIC EQUATIONS DIFFERENTIATION

PARAMETRIC EQUATIONS DIFFERENTIATION. WJEC PAST PAPER PROBLEM (OLD P3) JUNE 2003. PAST PAPER P3 JUNE 2003. A curve has parametric equations. Show that the tangent to the curve at the point P, whose parameter is p, has equation:.

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PARAMETRIC EQUATIONS DIFFERENTIATION

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  1. PARAMETRIC EQUATIONS DIFFERENTIATION WJEC PAST PAPER PROBLEM (OLD P3) JUNE 2003

  2. PAST PAPER P3 JUNE 2003 A curve has parametric equations Show that the tangent to the curve at the point P, whose parameter is p, has equation:

  3. First find the gradient of the tangent at the point where the parameter is p

  4. where the parameter is p we simply replace t with p This is the gradient of the TANGENT at the required point with parameter p

  5. The equation of the tangent is found using the standard equation of a straight line: Where t=p The equation of the tangent is

  6. So the equation of the TANGENT can be simplified to:

  7. THE QUESTION CONTINUES TO SAY: The tangent meets the x axis at A. Find the least value of the length OA, where O is the origin. When a line crosses the x axis we have the y coordinate as zero. USE y=0 in the equation of the tangent that we have just found.

  8. When y=0 Of course the x coordinate IS the distance OA This will be a least value when cos p=1(the most that cos p can be) Because the most denominator gives the least fraction.

  9. CONCLUDE BY SAYING: The least value of the distance OA is 2

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